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Localization of Gauge Theory on a Four-Sphere and Supersymmetric Wilson Loops

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We prove conjecture due to Erickson-Semenoff-Zarembo and Drukker-Gross which relates supersymmetric circular Wilson loop operators in the \({\mathcal N=4}\) supersymmetric Yang-Mills theory with a Gaussian matrix model. We also compute the partition function and give a new matrix model formula for the expectation value of a supersymmetric circular Wilson loop operator for the pure \({\mathcal N=2}\) and the \({\mathcal N=2^*}\) supersymmetric Yang-Mills theory on a four-sphere. A four-dimensional \({\mathcal N=2}\) superconformal gauge theory is treated similarly.

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  1. Physics Department, Princeton University, Princeton, NJ, 08544, USA

    Vasily Pestun

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  1. Vasily Pestun
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Communicated by N. A. Nekrasov

On leave of absence from ITEP, Moscow, 117259, Russia.

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Pestun, V. Localization of Gauge Theory on a Four-Sphere and Supersymmetric Wilson Loops. Commun. Math. Phys. 313, 71–129 (2012). https://doi.org/10.1007/s00220-012-1485-0

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